Mathematical analysis of a Dupuit-Richards model

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dc.contributor.authorAl Nazer, Safaa
dc.contributor.authorRosier, Carole
dc.contributor.authorTsegmid, Munkhgerel
dc.date.accessioned2023-03-30T17:00:20Z
dc.date.available2023-03-30T17:00:20Z
dc.date.issued2022-01-17
dc.description.abstractThis article concerns an alternative model to the 3D-Richards equation to describe the flow of water in shallow aquifers. The model couples the two dominant types of flow existing in the aquifer. The first is described by the classic Richards problem in the upper capillary fringe. The second results from Dupuit's approximation after vertical integration of the conservation laws between the bottom of the aquifer and the saturation interface. The final model consists of a strongly coupled system of parabolic-type partial differential equations that are defined in a time-dependent domain. First, we show how taking the low compressibility of the fluid into account eliminates the nonlinearity in the time derivative of the Richards equation. Then, the general framework of parabolic equations is used in non-cylindrical domains to give a global in time existence result to this problem.
dc.description.departmentMathematics
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAl Nazer, S., Rosier, C., & Tsegmid, M. (2022). Mathematical analysis of a Dupuit-Richards model. <i>Electronic Journal of Differential Equations, 2022</i>(06), pp. 1-22.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16510
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDupuit-Richards equations
dc.subjectFree boundary problems
dc.subjectGlobal solution
dc.subjectWeak solution
dc.subjectFluid flow modeling
dc.titleMathematical analysis of a Dupuit-Richards modelen_US
dc.typeArticle

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